def smallphi2(P, M, state, function, lambda1):
# calculates \phi for a specific system and returns: [\phi, minimum partition purview, minimum partition mechanism,
# purview]
# I have come across the following issue- the literature does not specify the order in which the two subfactorised
# matrices (here as left and right) should be produced to form the sigma comparable to rho
# for example if M={1,2,3} -> {1,3} U {2}, P = {1,2} -> {1} U {2} the optimal tensor product is far from obvious
# (to me)
Smallphi = 100
minpurv = {0, 1, 2}
minmech = {0, 1, 2}
rho = Repertoire2(P, M, state, function, lambda1)
for i in power_set(M):
for j in power_set(P):
left = Repertoire2(j, i, state, function, lambda1)
right = Repertoire2(P - j, M - i, state, function, lambda1)
sigma = np.kron(left, right)
if (Smallphi > D(rho, sigma)) and ([i, j] != [set(), set()]) and (
[M - i, P - j] != [set(), set()]):
Smallphi = D(rho, sigma)
minpurv = j
minmech = i
# this i think fixes the issue mentioned above
if P == {0, 1, 2} and j == {0, 2}:
sigma2 = BasisShift @ sigma @ BasisShift
if (Smallphi > D(rho, sigma2)):
Smallphi = D(rho, sigma2)
minpurv = j
minmech = i
return round(Smallphi, 10), minpurv, minmech, P
def ConceptStructure(lambda1, state):
concept1 = []
concept2 = []
for i in power_set({0, 1, 2}):
if i != set():
Core = []
Core2 = []
for function in ['cause', 'effect']:
Core.append(corecause(i, state[0], function[0]))
Core2.append(corecause2(i, lambda1, state[0], function[0]))
concept1.append([
min(Core[0][0], Core[1][0]), Core[0][3], Core[1][3], i,
state[0]
])
concept2.append([
min(Core2[0][0], Core2[1][0]), Core2[0][3], Core2[1][3], i,
state[0]
])
# these take the form phi, core cause, core effect, mechanism, state
Grep1 = 0
for j in range(len(concept1)):
a = concept1[j][0] * Repertoire(concept1[j][1], concept1[j][3],
concept1[j][4], 'c', True)
b = concept2[j][0] * Repertoire2(concept2[j][1], concept2[j][3],
concept2[j][4], 'c', lambda1, True)
c = concept1[j][0] * Repertoire(concept1[j][2], concept1[j][3],
concept1[j][4], 'e', True)
d = concept2[j][0] * Repertoire2(concept2[j][2], concept2[j][3],
concept2[j][4], 'e', lambda1, True)
Grep1 += 0.5 * (D(a, b) + D(c, d))
e = 1
return Grep1
def smallphi(P, M):
Smallphi = 100
minpurv = {1, 2, 3}
minmech = {0, 1, 2}
rho = Repertoire(P, M)
for i in power_set(M):
for j in power_set(P):
left = Repertoire(j, i)
right = Repertoire(P - j, M - i)
sigma = np.kron(left, right)
if (Smallphi > D(rho, sigma)) and ([i, j] != [set(), set()]) and ([M - i, P - j] != [set(), set()]):
Smallphi = D(rho, sigma)
minpurv = j
minmech = i
return round(Smallphi, 5), minpurv, minmech, P
def smallphi2(P, M, state, function, lambda1):
Smallphi = 1
minpurv = {0, 1, 2}
minmech = {0, 1, 2}
rho = Repertoire2(P, M, state, function, lambda1)
for i in power_set(M):
for j in power_set(P):
left = Repertoire2(j, i, state, function, lambda1)
right = Repertoire2(P - j, M - i, state, function, lambda1)
sigma = np.kron(left, right)
if (Smallphi > D(rho, sigma)) and ([i, j] != [set(), set()]) and (
[M - i, P - j] != [set(), set()]):
Smallphi = D(rho, sigma)
minpurv = j
minmech = i
return round(Smallphi, 15), minpurv, minmech, P
def corecause2(M, lambda1, state='o', function='c'):
placeholder = (0, 'no', 'concepts', 'here')
for j in power_set({0, 1, 2}):
if j != set():
trial = smallphi2(j, M, state, function, lambda1)
if trial[0] > placeholder[0]:
placeholder = trial
return placeholder
def corecause(M):
placeholder = (0, set(), set(), set())
for j in power_set({0,1}):
if j != set():
trial = smallphi(j, M)
if trial[0] > placeholder[0]:
placeholder = trial
return placeholder
def Phi(state):
CapitalPhi = [10, set()]
for i in power_set({0, 1, 2}):
if i != set() and i != {0, 1, 2}:
Distance = [
ConceptStructure(i, state), f"The MIP for state is {i}"
]
if Distance[0] < CapitalPhi[0]:
CapitalPhi = Distance
return CapitalPhi
def corecause2(M, state='o', function='c', lambda1=set()):
# this loops through all the possible purviews of a mechanism to find its core cause
# returns [\phi, minimum partition purview, minimum partition mechanism, purview]
placeholder = (0, 'no', 'concepts', 'here')
for j in power_set({0, 1, 2}):
if j != set():
trial = smallphi2(j, M, state, function, lambda1)
if trial[0] > placeholder[0]:
placeholder = trial
return placeholder
def ConceptStructure3(lambda1, state):
# to avoid creating classes i never actually create the Concept structure for a particular set up
# the first loop calculates the triple of [\phi, core cause, core effect] and attaches necessary
# information for the calculation of \Phi
concept1 = []
concept2 = []
for i in power_set({0, 1, 2}):
if i != set():
Core = []
Core2 = []
for function in ['cause', 'effect']:
Core.append(corecause2(i, state, function[0]))
Core2.append(corecause2(i, state, function[0], lambda1))
concept1.append(
[min(Core[0][0], Core[1][0]), Core[0][3], Core[1][3], i])
concept2.append(
[min(Core2[0][0], Core2[1][0]), Core2[0][3], Core2[1][3], i])
return concept1
def ConceptStructure(lambda1, state):
# to avoid creating classes i never actually create the Concept structure for a particular set up
# the first loop calculates the triple of [\phi, core cause, core effect] and attaches necessary
# information for the calculation of \Phi
concept1 = []
concept2 = []
for i in power_set({0, 1, 2}):
if i != set():
Core = []
Core2 = []
for function in ['cause', 'effect']:
Core.append(corecause2(i, state[0], function[0]))
Core2.append(corecause2(i, state[0], function[0], lambda1))
concept1.append([
min(Core[0][0], Core[1][0]), Core[0][3], Core[1][3], i,
state[0]
])
concept2.append([
min(Core2[0][0], Core2[1][0]), Core2[0][3], Core2[1][3], i,
state[0]
])
# these take the form \phi, core cause, core effect, mechanism, state
# this returns Grep1- the value of D(C(U),C(U_p)) for the p being lambda given as the input
# if speed is required in future we could halve computation time by calculating C(U) just once but for now its fast
# enough not to warrant bothering
Grep1 = 0
for j in range(len(concept1)):
a = concept1[j][0] * Repertoire2(concept1[j][1], concept1[j][3],
concept1[j][4], 'c', set(), True)
b = concept2[j][0] * Repertoire2(concept2[j][1], concept2[j][3],
concept2[j][4], 'c', lambda1, True)
c = concept1[j][0] * Repertoire2(concept1[j][2], concept1[j][3],
concept1[j][4], 'e', set(), True)
d = concept2[j][0] * Repertoire2(concept2[j][2], concept2[j][3],
concept2[j][4], 'e', lambda1, True)
Grep1 += 0.5 * (D(a, b) + D(c, d))
return Grep1
concept1[j][4], 'e', True)
d = concept2[j][0] * Repertoire2(concept2[j][2], concept2[j][3],
concept2[j][4], 'e', lambda1, True)
Grep1 += 0.5 * (D(a, b) + D(c, d))
e = 1
return Grep1
# for i in power_set({0,1,2}):
# print([ConceptStructure(i, 'o'), i])
concept1 = []
concept2 = []
for state in ['zero']:
for function in ['cause', 'effect']:
for i in power_set({0, 1, 2}):
if i != set():
Core = corecause(i, state[0], function[0])
Core2 = corecause(i, 'o', function[0])
concept1.append([Core[0], Core[3], i, state[0], function[0]])
concept2.append([Core2[0], Core2[3], i, 'o', function[0]])
# these take the form phi, core cause, mechanism, state, function
Grep1 = 0
for j in range(len(concept1)):
a = concept1[j][0] * Repertoire(concept1[j][1], concept1[j][2],
concept1[j][3], concept1[j][4], True)
b = concept2[j][0] * Repertoire(concept2[j][1], concept2[j][2],
concept2[j][3], concept2[j][4], True)
Grep1 += 0.5 * D(a, b)
e = 1
print(Grep1)
minmech = {0, 1, 2}
rho = Repertoire(P, M)
for i in power_set(M):
for j in power_set(P):
left = Repertoire(j, i)
right = Repertoire(P - j, M - i)
sigma = np.kron(left, right)
if (Smallphi > D(rho, sigma)) and ([i, j] != [set(), set()]) and ([M - i, P - j] != [set(), set()]):
Smallphi = D(rho, sigma)
minpurv = j
minmech = i
return round(Smallphi, 5), minpurv, minmech, P
def corecause(M):
placeholder = (0, set(), set(), set())
for j in power_set({0,1}):
if j != set():
trial = smallphi(j, M)
if trial[0] > placeholder[0]:
placeholder = trial
return placeholder
for i in power_set({0, 1}):
if i != set():
print([corecause(i), i])
# Repertoire({1,3},{1})
print(smallphi({0},{1}))